One-loop unitarity of scalar field theories on Poincare invariant commutative nonassociative spacetimes

TL;DR

This paper investigates scalar field theories on Poincare invariant commutative nonassociative spacetimes, demonstrating that they satisfy unitarity at one-loop level, unlike noncommutative theories, due to their unique non-locality features.

Contribution

It shows that scalar field theories on commutative nonassociative spacetimes preserve unitarity at one-loop, contrasting with noncommutative theories, and explores their non-locality properties.

Findings

One-loop self-energy diagrams satisfy Cutkosky rule.

Unitarity is preserved in these theories, unlike noncommutative counterparts.

Non-locality features may explain the unitarity properties.

Abstract

We study scalar field theories on Poincare invariant commutative nonassociative spacetimes. We compute the one-loop self-energy diagrams in the ordinary path integral quantization scheme with Feynman's prescription, and find that the Cutkosky rule is satisfied. This property is in contrast with that of noncommutative field theory, since it is known that noncommutative field theory with space/time noncommutativity violates unitarity in the above standard scheme, and the quantization procedure will necessarily become complicated to obtain a sensible Poincare invariant noncommutative field theory. We point out a peculiar feature of the non-locality in our nonassociative field theories, which may explain the property of the unitarity distinct from noncommutative field theories. Thus commutative nonassociative field theories seem to contain physically interesting field theories on deformed spacetimes.